The base of a triangle is the length of any of its sides. The height of a triangle is the perpendicular distance between the side whose length is the base and the vertex opposite that side.

NOTE BOOK

Words

Algebra

Area of a Triangle

A = bh12

Area of a triangle = • base • height12

h

b

Area of a Triangle10 2.

Finding the Area of a TriangleEXAMPLE 1

Find the area of the triangle shown.

11 ft

4 ft

A = bh12

Write the formula for the

area of a triangle.

Substitute 4 for b and 11 for h.

Simplify.

= bh12

= 22

ANSWER The area of the triangle is 22 square feet.

Area of a Triangle10 2.

• 4 • 11

Finding the Area of Combined FiguresEXAMPLE 2

Tall Ships A pattern of a sail for a tall ship is shown. How much material, in square feet, is needed to make the sail?

Find the area of each shape.

A = 6

ANSWER You will need 30 square feet of material to make the sail.

4 ft

6 ft

3 ftSOLUTION

1

2

Area of the triangle: Area of the rectangle:

A = • 4 • 312

A = 4 • 6

A = 24

Add the areas together to find the total area.

6 + 24 = 30

Area of a Triangle10 2.

A = • b • h12

Finding the Height of a TriangleEXAMPLE 3

The area of a triangle is 36 square inches and the base is 8 inches. What is the height of the triangle?

A = bh12

Write the formula for the area of a

triangle.

36 = 4 • h

Substitute 36 for A and 8 for b.

h = 36 4

Simplify.

Write a related division equation.

h = 9 Simplify.

ANSWER The height of the triangle is 9 inches.

Area of a Triangle10 2.

36 8